Computing Planar Swept Polygons Under Translation

A translational sweep is the translating of a polygon, called the generatrix G, around another polygon, called the directrix D, under two conditions: (1) G is always in contact with D; and (2) the interiors of G and D do not intersect. Three classes of translational sweep are studied, including the case in which both G and D are convex; the case in which G is convex, D monotone; and the case in which both are monotone. Efficient algorithms for computing the trajectory and the swept area as well as geometric and computational properties are presented for each class. A notion called the inverse generatrix, which reveals a duality between the trajectory and the swept polygon, is introduced to reduce complexity. (C) 1997 Elsevier Science Ltd. All rights reserved.